Context.In coded mask techniques, reconstructed sky images are
pseudo-images: they are maps of the correlation between the image recorded
on a detector and an array derived from the coded mask pattern.

Aims.The INTEGRAL /IBIS telescope provides images where the
flux of each detected source is given by the height of the local peak
in the correlation map. As such, it cannot provide an estimate of
the flux of an extended source. What is needed is intensity sky images
giving the flux per solide angle as typically done at other wavelengths.

Methods.In this paper, we present the response of the INTEGRAL IBIS /ISGRI coded
mask instrument to extended sources. We develop a general method
based on analytical calculations in order to measure the intensity and
the associated error of any celestial source and validated with Monte-Carlo
simulations.

Results.We find that the sensitivity degrades almost linearly with
the source extent. Analytical formulae are given as well as an easy-to-use
recipe for the INTEGRAL user. We check this method on IBIS /ISGRI data but
these results are general and applicable to any coded mask telescope.

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